Förstoringsglas
Sök Loader

Giuseppe Mastroianni & Gradimir Milovanovic 
Interpolation Processes 
Basic Theory and Applications

Stöd
Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that – peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., – sultsondivergentinterpolationprocesses, usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent – terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in thiseld (orthogonal polynomials, moduli of smoothness, K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.
€96.29
Betalningsmetoder

Innehållsförteckning

1. Constructive Elements and Approaches in Approximation Theory.- 1.1 Introduction to Approximation Theory.- 1.2 Basic Facts on Trigonometric Approximation.- 1.3 Chebyshev Systems and Interpolation.- 1.4 Interpolation by Algebraic Polynomials.- 2. Orthogonal Polynomials and Weighted Polynomial Approximation.- 2.1 Orthogonal Systems and Polynomials.- 2.2 Orthogonal Polynomials on the Real Line.- 2.3 Classical Orthogonal Polynomials.- 2.4 Nonclassical Orthogonal Polynomials.- 2.5 Weighted Polynomial Approximation.- 3. Trigonometric Approximation.- 3.1 Approximating Properties of Operators.- 3.2 Discrete Operators.- 4. Algebraic Interpolation in Uniform Norm.- 4.1 Introduction and Preliminaries.- 4.2 Optimal Systems of Nodes.- 4.3 Weighted Interpolation.- 5. Applications.- 5.1 Quadrature Formulae.- 5.2 Integral Equations.- 5.3 Moment-Preserving Approximation.- 5.4 Summation of Slowly Convergent Series.- References.- Index.

Om författaren

Gradimir V. Milovanovic is Professor of the University of Niš and Corresponding member of the Serbian Academy of Sciences and Arts.
Språk Engelska ● Formatera PDF ● Sidor 446 ● ISBN 9783540683490 ● Filstorlek 5.0 MB ● Utgivare Springer Berlin ● Stad Heidelberg ● Land DE ● Publicerad 2008 ● Nedladdningsbara 24 månader ● Valuta EUR ● ID 2162795 ● Kopieringsskydd Social DRM

Fler e-böcker från samma författare (r) / Redaktör

1 986 E-böcker i denna kategori